Asymmetric butterfly velocities in 2-local Hamiltonians

Abstract

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a "butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

16 pages, 8 figures

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• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Quantum Information Scrambling in Quantum Many-body Scarred Systems
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Scaling at the OTOC Wavefront: free versus chaotic models
• Integrability is generic in homogeneous U(1)-invariant nearest-neighbor qubit circuits
• Operator Spreading in the Memory Matrix Formalism
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Directional scrambling of quantum information in helical multiferroics